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The HY-2A satellite is the first ocean dynamic environment monitoring satellite of China. Centimeter-level radial accuracy is a fundamental requirement for its scientific research and applications. To achieve this goal, we designed the strategies of precise orbit determination (POD) in detail. To achieve the relative optimal orbit for HY-2A, we carried out POD using DORIS-only, SLR-only, and DORIS + SLR tracking data, respectively. POD tests demonstrated that the consistency level of DORIS-only and SLR-only orbits with respect to the CNES orbits were about 1.81 cm and 3.34 cm in radial direction in the dynamic sense, respectively. We designed 6 cases of different weight combinations for DORIS and SLR data, and found that the optimal relative weight group was 0.2 mm/s for DORIS and 15.0 cm for SLR, and RMS of orbit differences with respect to the CNES orbits in radial direction and three-dimensional (3D) were 1.37 cm and 5.87 cm, respectively. These tests indicated that the relative radial and 3D accuracies computed using DORIS + SLR data with the optimal relative weight set were obviously higher than those computed using DORIS-only and SLR-only data, and satisfied the requirement of designed precision. The POD for HY-2A will provide the invaluable experience for the following HY-2B, HY-2C, and HY-2D satellites.

A comparison between the Coupled Model Intercomparison Project Phase 5 (CMIP5) data and observations at 735 meteorological stations indicated that mean annual temperature (MAT) was underestimated about 1.8 °C while mean annual precipitation (MAP) was overestimated about 263 mm in general across the whole of China. A statistical analysis of China-CMIP5 data demonstrated that MAT exhibits spatial stationarity, while MAP exhibits spatial non-stationarity. MAT and MAP data from the China-CMIP5 dataset were downscaled by combining statistical approaches with a method for high accuracy surface modeling (HASM). A statistical transfer function (STF) of MAT was formulated using minimized residuals output by HASM with an ordinary least squares (OLS) linear equation that used latitude and elevation as independent variables, abbreviated as HASM-OLS. The STF of MAP under a BOX-COX transformation was derived as a combination of minimized residuals output by HASM with a geographically weight regression (GWR) using latitude, longitude, elevation and impact coefficient of aspect as independent variables, abbreviated as HASM-GB. Cross validation, using observational data from the 735 meteorological stations across China for the period 1976 to 2005, indicates that the largest uncertainty occurred on the Tibet plateau with mean absolute errors (MAEs) of MAT and MAP as high as 4.64 °C and 770.51 mm, respectively. The downscaling processes of HASM-OLS and HASM-GB generated MAEs of MAT and MAP that were 67.16% and 77.43% lower, respectively across the whole of China on average, and 88.48% and 97.09% lower for the Tibet plateau.

The increasing availability of big spatial data demands large-scale surface modeling methods. To find a solution for large-scale surface modeling problem, based on previously developed high accuracy surface modeling (HASM) method, an extended high accuracy surface modeling method utilizing cloud computing is developed. The developed method was run on a Hadoop-based cloud computing environment comprising four computers and applied for China’s Poyang Lake basin digital elevation model construction. The experiments results indicate that the cloud computing-based method outperforms the general sequential method based on single computer significantly and attains three times speedups. Furthermore, the improved schedule algorithm for cloud computing-based HASM has further accelerated the computing speed.

Airborne light detection and ranging (LiDAR) datasets with a large volume pose a great challenge to the traditional interpolation methods for the production of digital terrain models (DTMs). Thus, a fast, global interpolation method based on thin plate spline (TPS) is proposed in this paper. In the methodology, a weighted version of finite difference TPS is first developed to deal with the problem of missing data in the grid-based surface construction. Then, the interpolation matrix of the weighted TPS is deduced and found to be largely sparse. Furthermore, the values and positions of each nonzero element in the matrix are analytically determined. Finally, to make full use of the sparseness of the interpolation matrix, the linear system is solved with an iterative manner. These make the new method not only fast, but also require less random-access memory. Tests on six simulated datasets indicate that compared to recently developed discrete cosine transformation (DCT)-based TPS, the proposed method has a higher speed and accuracy, lower memory requirement, and less sensitivity to the smoothing parameter. Real-world examples on 10 public and 1 private dataset demonstrate that compared to the DCT-based TPS and the locally weighted interpolation methods, such as linear, natural neighbor (NN), inverse distance weighting (IDW), and ordinary kriging (OK), the proposed method produces visually good surfaces, which overcome the problems of peak-cutting, coarseness, and discontinuity of the aforementioned interpolators. More importantly, the proposed method has a similar performance to the simple interpolation methods (e.g., IDW and NN) with respect to computing time and memory cost, and significantly outperforms OK. Overall, the proposed method with low memory requirement and computing cost offers great potential for the derivation of DTMs from large-scale LiDAR datasets.

Separating ground from non-ground points is a challenging and essential task before the applications of airborne Light Detection And Ranging (LiDAR) data. The classical filters generally show good results on simple landscapes, but suffer from large filtering errors on complex landscapes with steep slopes and terrain discontinuities. To produce more satisfactory results over these landscapes, a scale-irrelevant and terrain-adaptive interpolation-based filter is presented in this paper. The contributions of the proposed method include a 1D spline-based algorithm for the collection of evenly distributed ground seeds as many as possible, a scale-irrelevant interpolation for estimating the heights of unclassified points and a terrain-adaptive elevation threshold to adapt to various terrain characteristics. The performance of the proposed method was first evaluated on the International Society Photogrammetry and Remote Sensing (ISPRS) benchmark dataset. Results show that the proposed method with the average total error of 2.70% and kappa coefficient of 90.84% outperforms the existing filtering algorithms developed in recent decade (2010–2020). The performance of the proposed method was further assessed on four high-density airborne LiDAR point clouds located in urban and forested sites and compared with four state-of-the-art filters including progressive morphological filter (PMF), cloth simulation filter (CSF), progressive TIN densification (PTD) and multiresolution hierarchical filter (MHF). Results demonstrate that the proposed method is averagely more accurate than the well-known filters in terms of total error and kappa coefficient, and much faster than PTD and MHF. Moreover, the proposed method produces more satisfactory DEMs than the classical methods.

A digital elevation model (DEM) derived from remote sensing data often suffers from outliers due to various reasons such as the physical limitation of sensors and low contrast of terrain textures. In order to reduce the effect of outliers on DEM construction, a robust algorithm of multiquadric (MQ) methodology based on M-estimators (MQ-M) was proposed. MQ-M adopts an adaptive weight function with three-parts. The weight function is null for large errors, one for small errors and quadric for others. A mathematical surface was employed to comparatively analyze the robustness of MQ-M, and its performance was compared with those of the classical MQ and a recently developed robust MQ method based on least absolute deviation (MQ-L). Numerical tests show that MQ-M is comparative to the classical MQ and superior to MQ-L when sample points follow normal and Laplace distributions, and under the presence of outliers the former is more accurate than the latter. A real-world example of DEM construction using stereo images indicates that compared with the classical interpolation methods, such as natural neighbor (NN), ordinary kriging (OK), ANUDEM, MQ-L and MQ, MQ-M has a better ability of preserving subtle terrain features. MQ-M replaces thin plate spline for reference DEM construction to assess the contribution to our recently developed multiresolution hierarchical classification method (MHC). Classifying the 15 groups of benchmark datasets provided by the ISPRS Commission demonstrates that MQ-M-based MHC is more accurate than MQ-L-based and TPS-based MHCs. MQ-M has high potential for DEM construction.

A high accuracy surface modeling method (HASM) has been developed to provide a solution to many surface modeling problems such as DEM construction, surface estimation and spatial prediction. Although HASM is able to model surfaces with a higher accuracy, its low computing speed limits its popularity in constructing large scale surfaces. Hence, the research described in this article aims to improve the computing efficiency of HASM with a graphic processor unit (GPU) accelerated multi-grid method (HASM-GMG). HASM-GMG was tested with two types of surfaces: a Gauss synthetic surface and a real-world example. Results indicate that HASM-GMG can gain significant speedups compared with CPU-based HASM without acceleration on GPU. Moreover, both the accuracy and speed of HASM-GMG are superior to the classical interpolation methods including Kriging, Spline and IDW.

Ship-borne global navigation satellite system (GNSS) technique can overcome the weakness of satellite altimetry and tide gauge in measuring sea surface heights (SSHs) over coastal seas. Ship-borne GNSS technique can be used to calibrate SSHs determined by the satellite altimetry and tide gauge. The ship-borne GNSS data are processed with the single-epoch precise point positioning (PPP) method to estimate SSHs which are filtered by the Gaussian filter to weaken and/or remove effects of sea wind and wave field. Tidal corrections are also taken into consideration to improve SSHs. One crossover adjustment method is put forward to calculate the bias and drift along the ship route and assess the accuracy of SSHs. We processed the in-situ ship-borne GPS data over the offshore sea around Keelung to compute precisely SSHs with the single-epoch PPP. Statistical results of SSH differences of crossover points indicate that the root mean squares error of SSHs determined by the ship-borne GPS is up to level of 12.9 cm over the offshore sea ~30 km far away to land.

Support vector machine for regression (SVR) is an efficient tool for solving function estimation problem. However, it is sensitive to outliers due to its unbounded loss function. In order to reduce the effect of outliers, we propose a robust SVR with a trimmed Huber loss function (SVRT) in this paper. Synthetic and benchmark datasets were, respectively, employed to comparatively assess the performance of SVRT, and its results were compared with those of SVR, least squares SVR (LS-SVR) and a weighted LS-SVR. The numerical test shows that when training samples are subject to errors with a normal distribution, SVRT is slightly less accurate than SVR and LS-SVR, yet more accurate than the weighted LS-SVR. However, when training samples are contaminated by outliers, SVRT has a better performance than the other methods. Furthermore, SVRT is faster than the weighted LS-SVR. Simulating eight benchmark datasets shows that SVRT is averagely more accurate than the other methods when sample points are contaminated by outliers. In conclusion, SVRT can be considered as an alternative robust method for simulating contaminated sample points.

Digital elevation model (DEM) source data are subject to both horizontal and vertical errors owing to improper instrument operation, physical limitations of sensors, and bad weather conditions. These factors may bring a negative effect on some DEM-based applications requiring low levels of positional errors. Although classical smoothing interpolation methods have the ability to handle vertical errors, they are prone to omit horizontal errors. Based on the statistical concept of the total least squares method, a total error-based multiquadric (MQ-T) method is proposed in this paper to reduce the effects of both horizontal and vertical errors in the context of DEM construction. In nature, the classical multiquadric (MQ) method is a vertical error regression procedure, whereas MQ-T is an orthogonal error regression model. Two examples, including a numerical test and a real-world example, are employed in a comparative performance analysis of MQ-T for surface modeling of DEMs. The numerical test indicates that...

The classification of airborne laser scanning ALS point clouds is a necessary step in the process of digital elevation model DEM construction. Motivated by the surface interpolation filtering scheme, a multi-resolution hierarchical classification MHC method was developed to perform classification in our previous research. However, similar to almost all filtering methods, MHC suffers from the problem of misclassifying off-terrain and ground points in complex landscapes with steep slopes and large discontinuities. To improve the classification accuracy in the above landscapes, the original MHC is improved in this article by adopting a region growing-based segmentation method to maximally capture the initial ground seeds of MHC. Furthermore, considering the high sensitivity of principle component analysis PCA to outliers, a robust PCA approach based on least trimmed squares LTS is proposed to estimate point normals. Fifteen groups of data sets provided by the International Society for Photogrammetry and Remote Sensing ISPRS Working Group III/3 are utilized to compare the performances of the improved and original MHCs. Results indicate that the improved MHC is more accurate than the original MHC, irrespective of accuracy measures. In addition, we also compare the results of our method with three new filtering methods developed in the years 2013 and 2014. It is found that regardless of landscapes i.e. urban and rural samples, the improved MHC is averagely more accurate than the three filtering methods in terms of type II error, and irrespective of accuracy measures i.e. types I, II and total errors, our method outperforms the three filtering methods for the rural samples. In short, the robust segmentation-based MHC demonstrates great potential to ALS-derived DEM construction in rural areas.

The General Circulation Models and Coupled Model Intercomparison Project Phase 5 (CMIP5) datasets used for the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) painted future opportunities and challenges afforded by climate change with broad strokes. The model outputs incorporate substantial uncertainty due to the relatively coarse spatial scales and the complexity of the processes incorporated in these models and as a consequence, it is difficult to predict future trends and infrastructure needs in large countries like China at local and regional scales over the next century. The work reported in this article describes several statistical transfer functions that were used to downscale CMIP5 climate predictions in China. The original and new downscaled CMIP5 predictions are compared with observations from 735 meteorological stations scattered across China for the period 2006–2015 to show the various improvements achieved with downscaling. Comparing the three RCP scenarios (2.6, 4.5 and 8.5) during the period 2006–2015 with observations from 735 meteorological stations indicates that MAEs of mean annual temperature were 1.9 °C for China on average and that the actual temperature was under-estimated at 87% of the meteorological stations under all three scenarios. After the downscaling process using a High Accuracy Surface Modeling (HASM)-based method, the MAEs for mean annual temperature under the three scenarios were reduced to 0.62 °C for China on average. The MAEs of annual mean precipitation were 317.29, 315.24 and 315.49 mm under the RCP2.6, RCP4.5, and RCP8.5 scenarios, respectively for China on average and the actual precipitation was over-estimated by all three scenarios at approximately 75% of the meteorological stations. The HASM-based downscaling process meant that the MAEs for the three scenarios were reduced to 80–85 mm for China on average. The downscaled predictions are used to show how temperature and precipitation are likely to vary by region in China from 2011 to 2100. The downscaled results suggest that most of China will become warmer and wetter on average under all three scenarios over the next 30 years and provide improved information to guide the investments and actions that will be needed to improve climate change resilience across China's varied landscapes in the 21st century.

In most cases, climate change projections from General Circulation Models (GCM) and Regional Climate Models cannot be directly applied to climate change impact studies, and downscaling is, therefore, needed. A large number of statistical downscaling methods exist, but no clear recommendations exist of which methods are more appropriate, depending on the application. This paper compares two different statistical downscaling methods, Presim1 and Presim2, using the Coupled Model Intercomparison Project Phase 5 (CMIP5) datasets and station observations. Both methods include two steps, but the major difference between them is how the CMIP5 dataset and the station data used. The downscaled precipitation data are validated with observations through China and Jiangxi province from 1976 to 2005. Results show that GCMs cannot be used directly in climate change impact studies. In China, the second method Presim2, which establishes regression model based on the station data, has a tendency to overestimate or underestimate the real values. The accuracy of Presim1 is much better than Presim2 based on mean absolute error, mean relative error and root mean square error. Presim1 fuses the mode data and station data effectively. Results also show the importance of the meteorological station data in the process of residual modification.

Light detection and ranging (LiDAR) technique is currently one of the most important tools for collecting elevation points with a high density in the context of digital elevation model (DEM) construction. However, the high density data always leads to serious time and memory consumption problems in data processing. In this paper, we have developed a thin plate spline (TPS)-based feature-preserving (TPS-F) method for LiDAR-derived ground data reduction by selecting a certain amount of significant terrain points and by extracting geomorphological features from the raw dataset to maintain the accuracy of constructed DEMs as high as possible, while maximally keeping terrain features. We employed four study sites with different topographies (i.e., flat, undulating, hilly and mountainous terrains) to analyze the performance of TPS-F for LiDAR data reduction in the context of DEM construction. These results were compared with those of the TPS-based algorithm without features (TPS-W) and two classical data selection methods including maximum z-tolerance (Max-Z) and the random method. Results show that irrespective of terrain characteristic, the two versions of TPS-based approaches (i.e., TPS-F and TPS-W) are always more accurate than the classical methods in terms of error range and root means square error. Moreover, in terms of streamline matching rate (SMR), TPS-F has a better ability of preserving geomorphological features, especially for the mountainous terrain. For example, the average SMR of TPS-F is 89.2% in the mountainous area, while those of TPS-W, max-Z and the random method are 56.6%, 34.7% and 35.3%, respectively.

Irrigation water demand accounts for more than 95% of the total water use in the Kaidu-kongqi River Basin. Determination of the spatial and temporal trends in irrigation water demand is important for making sustainable and wise water management strategies in this highly water deficit region. In this study, the spatial and temporal trends in irrigation water demand as well as net crop irrigation water requirements for nine major crops during 1985–2009 were analyzed by combining the Penman-Monteith equation recommended by Food and Agriculture Organization (FAO) and GIS technology. The regional water stress was also evaluated based on the total irrigation water demand and river discharge at the annual and monthly scales. The results indicated that the annual irrigation water demand in this arid region showed a significant increasing trend during the past 25 years. Total irrigation water demand increased from 14.68 × 108 m3 in 1985 to 34.15 × 108 m3 in 2009. The spatial pattern of total irrigation water demand was significantly affected by the changes in cotton growing area. Due to differences in crop planting structure, the monthly average irrigation water demands in Korla City and Yuli County amounted to the peak in July, while those in other regions reached the maximum in June. Although the annual river runoff was much larger than the irrigation water demand, there was serious water deficit during the critical water use period in May and June in some dry years. The presented study provides important information for managers and planners on sustainable use of water resources in this arid region.

Ground observation is able to obtain highly accurate data with high temporal resolution at observation points, but these observation points are too sparsely to satisfy the application requirements at regional scale. Satellite remote sensing can frequently supply spatially continuous information on earth surface, which is impossible from ground-based investigations, but remote sensing description is not able to directly obtain process parameters. In fact, in terms of fundamental theorem of surfaces, a surface is uniquely defined by the first fundamental coefficients, about the details of the surface observed when we stay on the surface, and the second fundamental coefficients, the change of the surface observed from outside the surface. A method for high accuracy surface modeling (HASM) has been developed initiatively to find solutions for error problem and slow-speed problem of earth surface modeling since 1986. HASM takes global approximate information (e.g., remote sensing images or model simulation results) as its driving field and local accurate information (e.g., ground observation data and/or sampling data) as its optimum control constraints. Its output satisfies the iteration stopping criterion which is determined by application requirement for accuracy. This paper reviews problems to be solved in every development stage and applications of HASM.

A new greedy-based multiquadric method (MQ-G) has been developed to perform LiDAR-derived ground data reduction by selecting a certain amount of significant terrain points from the raw dataset to keep the accuracy of the constructed DEMs as high as possible, while maximally retaining terrain features. In the process of MQ-G, the significant terrain points were selected with an iterative process. First, the points with the maximum and minimum elevations were selected as the initial significant points. Next, a smoothing MQ was employed to perform an interpolation with the selected critical points. Then, the importance of all candidate points was assessed by interpolation error (i.e. the absolute difference between the interpolated and actual elevations). Lastly, the most significant point in the current iteration was selected and used for point selection in the next iteration. The process was repeated until the number of selected points reached a pre-set level or no point was found to have the interpolation error exceeding a user-specified accuracy tolerance. In order to avoid the huge computing cost, a new technique was presented to quickly solve the systems of MQ equations in the global interpolation process, and then the global MQ was replaced with the local one when a certain amount of critical points were selected. Four study sites with different morphologies (i.e. flat, undulating, hilly and mountainous terrains) were respectively employed to comparatively analyze the performances of MQ-G and the classical data selection methods including maximum z-tolerance (Max-Z) and the random method for reducing LiDAR-derived ground datasets. Results show that irrespective of the number of selected critical points and terrain characteristics, MQ-G is always more accurate than the other methods for DEM construction. Moreover, MQ-G has a better ability of preserving terrain feature lines, especially for the undulating and hilly terrains.

Remote-sensing-derived elevation data sets often suffer from noise and outliers due to various reasons, such as the physical limitations of sensors, multiple reflectance, occlusions and low contrast of texture. Outliers generally have a seriously negative effect on DEM construction. Some interpolation methods like ordinary kriging (OK) are capable of smoothing noise inherent in sample points, but are sensitive to outliers. In this paper, a robust algorithm of multiquadric method (MQ) based on an Improved Huber loss function (MQ-IH) has been developed to decrease the impact of outliers on DEM construction. Theoretically, the improved Huber loss function is null for outliers, quadratic for small errors, and linear for others. Simulated data sets drawn from a mathematical surface with different error distributions were employed to analyze the robustness of MQ-IH. Results indicate that MQ-IH obtains a good balance between efficiency and robustness. Namely, the performance of MQ-IH is comparative to those of the classical MQ and MQ based on the Classical Huber loss function (MQ-CH) when sample points follow a normal distribution, and the former outperforms the latter two when sample points are subject to outliers. For example, for the Cauchy error distribution with the location parameter of 0 and scale parameter of 1, the root mean square errors (RMSEs) of MQ-CH and the classical MQ are 0.3916 and 1.4591, respectively, whereas that of MQ-IH is 0.3698. The performance of MQ-IH is further evaluated by qualitative and quantitative analysis through a real-world example of DEM construction with the stereo-images-derived elevation points. Results demonstrate that compared with the classical interpolation methods, including natural neighbor (NN), OK and ANUDEM (a program that calculates regular grid digital elevation models (DEMs) with sensible shape and drainage structure from arbitrarily large topographic data sets), and two versions of MQ, including the classical MQ and MQ-CH, MQ-IH has a better ability of maximally reducing the impact of outliers, while faithfully preserving terrain features. Theoretically, MQ-IH is not a promising interpolation method, and some side effects can be found from its simulation results. For example, the contours of MQ-IH are coarser than ANUDEM in some locations of the real-world study site, and its hill shade may not strictly agree with the real-world surface at rough terrain. Furthermore, the computing cost of MQ-IH is much bigger than that of the classical interpolation methods. However, compared with the classical interpolation methods, MQ-IH has significant potential for interpolating remote-sensing-derived elevation data sets.

In order to find a solution for accurate, topographic data-demanding applications, such as catchment hydrologic modeling and assessments of anthropic activities impact on environmental systems, high-accuracy surface modeling (HASM) method is developed. Although it can produce a digital elevation model (DEM) surface of higher accuracy than classical methods, e.g. inverse distance weighted, spline and kriging, HASM requires numerous iterations to solve large linear systems, which impede its applications in high-resolution and large-scale surface interpolation. This paper aims to demonstrate the utilization of graphics’ processing units (GPUs) device to accelerate HASM in constructing large-scale and high-resolution DEM surfaces. We parallelized the linear system algorithm for solving HASM with Compute Unified Device Architecture, a parallel programming model developed by NVIDIA. We designed a memory-saving strategy to enable the HASM algorithm to run on GPUs. The speedup ratio of GPU-based algorithm was tested and compared with CPU-based algorithm through simulations of both ideal Gaussian synthetic surface and real topographic surface in the loess plateau of Gansu province. The GPU-parallelized algorithm can attain an over 10× speedup ratio with the CPU-based algorithm as a reference. The speedup ratio increases with the scale and resolution of the dataset. The memory management strategy efficiently reduces the memory usage by more than eight times the grid cell number. Implementing HASM in the GPUs device enables modeling large-scale and high-resolution surfaces in a reasonable time period and implies the potential benefits from the use of GPUs as massive, parallel co-processors for arithmetic-intensive data-processing applications.

The inverse-distance weighting (IDW) method is considered as one of the most popular deterministic methods and is widely applied to a variety of areas because of its low computational cost and easy implementation. In this paper, we show that the classical IDW is essentially a zeroth-order local kernel regression method with an inverse distance weight function. Thus, it suffers from various shortcomings, such as the boundary bias. Considering the advantages of the local polynomial modeling technique in statistics, the classical IDW was generalized into a higher-order regression by the Taylor expansion and then computed by means of a weighted least-squares method. Surface modeling of rainfall fields in China indicated that the generalized IDWs with the first- and second-orders are more accurate than the classical IDW in terms of root mean square error (RMSE). The example of digital elevation model construction with a group of sample points showed that the two generalized IDWs have better RMSE and mean error than the classical IDW. Furthermore, the second-order IDW has a better performance than the ordinary kriging in terms of RMSE. A theoretical analysis demonstrated that the gradient-plus-inverse distance squared method presented by Nalder and Wein (Agric For Meteorol 92(4): 211-225, 1998) is a first-order form of the generalized IDW expanded on spatial coordinates and elevation. In a word, the generalized IDW can incorporate multiple covariates, which can better explain the interpolation procedure and might improve its accuracy.

Data pits commonly appear in lidar-derived canopy height models (CHMs) owing to the penetration ability of airborne light detection and ranging (lidar) into tree crowns. They have a seriously negative effect on the quality of tree detection and subsequent biophysical measurements. In this study, we propose an algorithm based on robust locally weighted regression and robust z-scores for the construction of a pit-free CHM. A significant advantage of the new algorithm is that it is parameter free, which makes it efficient and robust for practical applications. Simulated and airborne lidar-derived data sets are employed to assess the performance of the new method for CHM construction, and its results are compared to those of three classical methods, namely the natural neighbor (NN) interpolation of the highest point method (HPM), mean filter, and median filter. The results from the simulated data set demonstrate that our algorithm is more accurate compared to the three classical methods for generating pit-free CHMs in the presence of data pits. CHM construction using the lidar-derived data set shows that, compared to the classical methods, the new method has a better ability to remove data pits as well as preserving the edges, shapes, and structures of canopy gaps and crowns. Moreover, the proposed method performs better compared to the classical methods in deriving plot-level maximum tree heights from CHMs. Thus, the new method shows high potential for pit-free CHM construction.

The sensitivities of the initial value and the sampling information to the accuracy of a high accuracy surface modeling (HASM) are investigated and the implementations of this new modeling method are modified and enhanced. Based on the fundamental theorem of surface theory, HASM is developed to correct the error produced in geographical information system and ecological modeling process. However, the earlier version of HASM is theoretically incomplete and its initial value must be produced by other surface modeling methods, such as spline, which limit its promotion. In other words, we must use other interpolators to drive HASM. According to the fundamental theorem of surface theory, we modify HASM, namely HASM.MOD, by adding another important nonlinear equation to make it independent of other methods and, at the same time, have a complete and solid theory foundation. Two mathematic surfaces and monthly mean temperature of 1951-2010 are used to validate the effectiveness of the new method. Experiments show that the modified version of HASM is insensitive to the selection of initial value which is particular important for HASM. We analyze the sensitivities of sampling error and sampling ratio to the simulation accuracy of HASM.MOD. It is found that sampling information plays an important role in the simulation accuracy of HASM.MOD. Another feature of the modified version of HASM is that it is theoretically perfect as it considers the third equation of the surface theory which reflects the local warping of the surface. The modified HASM may be useful with a wide range of spatial interpolation as it would no longer rely on other interpolation methods.

Since spatial datasets are subject to sampling errors, a smoothing interpolation method should be employed to remove noise during DEM construction. Although least squares support vector machines (LSSVM) have been widely accepted as a classifier, their effect on smoothing noisy data is almost unknown. In this article, the smoothness of LSSVM was explored, and its effect on smoothing noisy data in DEM construction was tested. In order to improve the ability to deal with large datasets, a local method of LSSVM has been developed, where only the neighboring sampling points around the one to be estimated are used for computation. A numerical test indicated that LSSVM is more accurate than the classical smoothing methods including TPS and kriging, and its error surfaces are more evenly distributed. The real-world example of smoothing noise inherent in lidar-derived DEMs also showed that LSSVM has a positive smoothing effect, which is approximately as accurate as TPS. In short, LSSVM with a high efficiency can be considered as an alternative smoothing method for smoothing noisy data in DEM construction.

Thin plate spline (TPS) has been widely accepted as a method for smooth fitting of noisy data. However, the classical TPS always has an ill-conditioning problem when two sample points are very close. Although the modified orthogonal least squares-based TPS (TPS-M) avoids this ill-conditioning problem, it is not completely immune to over-fitting when sample points are noisy. In this paper, a regularized least squares method of thin plate spline (TPS-RLS) was developed, which adds a weight penalty term to the error criterion of orthogonal least squares (OLS). TPS-RLS combines the advantages of both regularization and OLS, which avoid the over-fitting and the ill-conditioning problems simultaneously. Numerical tests indicate that irrespective of the standard deviation of sampling errors and the number of knots, TPS-RLS is always more accurate than TPS-M for smooth fitting of noisy data, whereas TPS-M would have a serious over-fitting problem if the optimal number of knots were not determined in advance. The real-world example of fitting total station instrument data shows that among the classical interpolation methods including IDW, natural neighbor and ordinary kriging, TPS-RLS has the highest accuracy for a series of DEMs with different resolutions, especially for the coarse one. Surface modeling of DEMs with contour lines demonstrate that TPS-RLS has a better performance than the classical methods in terms of both root mean squared error and relief shaded map appearance.

We presented a multiresolution hierarchical classification (MHC) algorithm for differentiating ground from non-ground LiDAR point cloud based on point residuals from the interpolated raster surface. MHC includes three levels of hierarchy, with the simultaneous increase of cell resolution and residual threshold from the low to the high level of the hierarchy. At each level, the surface is iteratively interpolated towards the ground using thin plate spline (TPS) until no ground points are classified, and the classified ground points are used to update the surface in the next iteration. 15 groups of benchmark dataset, provided by the International Society for Photogrammetry and Remote Sensing (ISPRS) commission, were used to compare the performance of MHC with those of the 17 other publicized filtering methods. Results indicated that MHC with the average total error and average Cohen’s kappa coefficient of 4.11% and 86.27% performs better than all other filtering methods.

A sequential adjustment (SA) method is employed to decrease the computational cost of high-accuracy surface modeling (HASM), and the SA of HASM (HASM-SA) is being developed. A mathematical surface was used to comparatively analyze the computing speed of SA and the classical iterative solvers provided by MATLAB 7.7 for solving the system of linear equations of HASM. Results indicate that SA is much faster than the classical iterative solvers. The computing time of HASM-SA is determined by not only the total number of grid cells but also the number of sampling points in the computational domain. A real-world example of surface modeling of digital elevation models (DEMs) with various resolutions shows that HASM-SA is averagely more accurate and much faster than the commonly used interpolation methods, such as inverse distance weighting (IDW), kriging, and three versions of spline, namely regularized spline (RSpline), thin-plate spline (TPS), and ANUDEM in terms of root mean square error (RMSE), mean absolute...

To smooth noises inherent in uniformly sampled dataset, the smoothness of high accuracy surface modeling HASM was explored, and a smoothing method of HASM HASM-SM was developed based on a penalized least squares method. The optimal smoothing parameter of HASM-SM was automatically obtained by means of the generalized cross-validation GCV method. For an efficient smoothing computation, discrete cosine transform was employed to solve the system of HASM-SM and to estimate the minimum GCV score, simultaneously. Two examples including a numerical test and a real-world example were employed to compare the smoothing ability of HASM-SM with that of GCV thin plate smoothing spline TPS and kriging. The numerical test indicated that the minimum GCV HASM-SM is averagely more accurate than TPS and kriging for noisy surface smoothing. The real-world example of smoothing a lidar-derived Digital Elevation Model DEM showed that HASM-SM has an obvious smoothing effect, which is on a par with TPS. In conclusion, HASM-SM provides an efficient tool for filtering noises in grid-based surfaces like remote sensing–derived images and DEMs.

We have found that a spatial interpolation of mean annual temperature (MAT) in China can be accomplished using a global ordinary least squares regression model since the relationship between temperature and its environmental determinants is constant. Therefore the estimation of MAT does not very across space and thus exhibits spatial stationarity. The interpolation of mean annual precipitation (MAP), however, is more complex and changes spatially as a function of topographic variation. Therefore, MAP shows spatial non-stationarity and must be estimated with a geographically weighted regression. A statistical transfer function (STF) of MATwas formulated using minimized residuals output from a high accuracy and high speed method for surface modeling (HASM) with an ordinary least squares (OLS) linear equation that uses latitude and elevation as independent variables, abbreviated as HASM- OLS. The STF of MAP under a BOX-COX transformation is derived as a combination of minimized residuals output by HASM with a geographically weighted regression (GWR) using latitude, longitude, elevation, impact coefficient of aspect and sky view factor as independent variables, abbreviated as HASM-GWR-BC. In terms of HASM-OLS and HASM-GWR-BC

The multiquadric method (MQ) with high interpolation accuracy has been widely used for interpolating spatial data. However, MQ is an exact interpolation method, which is improper to interpolate noisy sampling data. Although the least squares MQ (LSMQ) has the ability to smooth out sampling errors, it is inherently not robust to outliers due to the least squares criterion in estimating the weights of sampling knots. In order to reduce the impact of outliers on the accuracy of digital elevation models (DEMs), a robust method of MQ (MQ-R) has been developed. MQ-R includes two independent procedures: knot selection and the solution of the system of linear equations. The two independent procedures were respectively achieved by the space-filling design and the least absolute deviation, both of which are very robust to outliers. Gaussian synthetic surface, which is subject to a series of errors with different distributions, was employed to compare the performance of MQ-R with that of LSMQ. Results indicate that LSMQ is seriously affected by outliers, whereas MQ-R performs well in resisting outliers, and can construct satisfactory surfaces even though the data are contaminated by severe outliers. A real-world example of DEM construction was employed to evaluate the robustness of MQ-R, LSMQ, and the classical interpolation methods including inverse distance weighting method, thin plate spline, and ANUDEM. Results showed that compared with the classical methods, MQ-R has the highest accuracy in terms of root mean square error. In conclusion, when sampling data is subject to outliers, MQ-R can be considered as an alternative method for DEM construction.

A new method based on orthogonal least square OLS of multiquadric algorithm MOLS is proposed for digital elevation model DEM generalization by the retrieval of critical points from a grid-based DEM to construct a triangulated irregular network surface. The focus is on the method for accurately obtaining the critical points, which maximally retain the important terrain feature lines. The grid-based DEM to be generalized is first approximated in terms of multiquadric method, and then the significances of the grids are assessed based on OLS method with the merit that each selected grid point gives the maximal increment to the explained variance of the desired output. We used six study sites with different terrain complexities to comparatively analyze the generalization accuracies of MOLS and the classical methods including very important method and point-additive method Latticetin under different numbers of retrieved significant points. The results indicate that MOLS averagely performs better than the classical methods for the original DEM generalization in terms of root mean square error. The analytical results also show that MOLS has the better ability in maintaining the feature lines inherent in the original DEM than the classical methods in terms of streamline matching rate. The perfect performance of the newly proposed method can be attributed to the high accuracy of multiquadric method for surface approximation and the effectiveness of OLS for point significance assessment.

Changes in precipitation could have crucial influences on the regional water resources in arid regions such as Xinjiang. It is necessary to understand the intrinsic multi-scale variations of precipitation in different parts of Xinjiang in the context of climate change. In this study, based on precipitation data from 53 meteorological stations in Xinjiang during 1960–2012, we investigated the intrinsic multi-scale characteristics of precipitation variability using an adaptive method named ensemble empirical mode decomposition (EEMD). Obvious non-linear upward trends in precipitation were found in the north, south, east and the entire Xinjiang. Changes in precipitation in Xinjiang exhibited significant inter-annual scale (quasi-2 and quasi-6 years) and inter-decadal scale (quasi-12 and quasi-23 years). Moreover, the 2–3-year quasi-periodic fluctuation was dominant in regional precipitation and the inter-annual variation had a considerable effect on the regional-scale precipitation variation in Xinjiang. We also found that there were distinctive spatial differences in variation trends and turning points of precipitation in Xinjiang. The results of this study indicated that compared to traditional decomposition methods, the EEMD method, without using any a priori determined basis functions, could effectively extract the reliable multi-scale fluctuations and reveal the intrinsic oscillation properties of climate elements.

Geostatistical characterization of local DEM error is usually based on the assumption of a stationary variogram model which requires the mean and variance to be finite and constant in the area under investigation. However, in practice this assumption is appropriate only in a restricted spatial location, where the local experimental variograms vary slowly. Therefore, an adaptive method is developed in this article to model non-stationary variograms, for which the estimator and the indicator for characterization of spatial variation are a Voronoi map and the standard deviation of mean values displayed in the Voronoi map, respectively. For the adaptive method, the global domain is divided into different meshes with various sizes according to the variability of local variograms. The adaptive method of non-stationary variogram modeling is applied to simulating error surfaces of a LiDAR derived DEM located in Sichuan province, China. Results indicate that the locally adaptive variogram model is more accurate than the global one for capturing the characterization of spatial variation in DEM errors. The adaptive model can be considered as an alternative approach to modeling non-stationary variograms for DEM error surface simulation.

A new method for filling voids is developed by improving the approach to high-accuracy surface modelling (HASM), which is based on the first fundamental coefficients and the second fundamental coefficients of surfaces. The first fundamental coefficients are used to calculate the lengths of curves, angles of tangent vectors, areas of regions and geodesics on the surface. The second fundamental coefficients reflect the local warping of the surface, namely its deviation from the tangent plane at the point under consideration, which can be observed from outside the Earth. Nine regions with different landform complexities in hilly, plateau and mountainous areas are selected for testing the performance of HASM by comparing those ones of the classic methods such as triangulated irregular network (TIN), inverse distance weighted interpolation (IDW), advanced Spline method (ANUDEM), Spline and Kriging. The results demonstrated that the HASM void filling always has the highest accuracy regardless of the landform complexity, void area and auxiliary data.

We have presented a new method for generating grid-based digital elevation models (DEMs) based on Coons patch. A series of Gaussian synthetic surfaces with various surface complexities were employed to comparatively analyze the simulation accuracies of Coons patch and the classical interpolation methods, such as IDW, Natural neighbor, SPLINE and KRIGING. Results indicate that irrespective of terrain complexity, Coons patch is much more accurate than the classical interpolation methods, and the accuracy of Coons patch is about 327.30, 15.19, 3.66 and 40.07 times as high as the accuracies of IDW, Natural neighbor, SPLINE and KRIGING on average. A real-world test area was used to test the effect of sampling density on the simulation accuracy. The results indicate that Coons patch has a higher accuracy than the classical interpolation methods regardless of sampling density. In a word, Coons patch as an accurate interpolation method can be used for grid-based DEM construction.

A robust estimator based on the M-estimation principle (REMP) has been developed for digital elevation model (DEM) accuracy assessment. Adaptive weights were employed to respond to a broad class of DEM error distributions, and an iterative procedure in terms of REMP starting from robust initial estimates with a high breakdown point was introduced. Original DEMs with the resolution of 2 m were obtained by means of light detection and Ranging (LiDAR) from two study sites. DEM errors in each study site were, respectively, calculated based on 100 checkpoints captured by real-time kinematic (RTK) in terms of stratified random sampling strategy. Each group of DEM errors was, respectively, contaminated by five groups of outliers from different distributions. Thus, ten groups of simulated DEM errors were employed to comparatively assess the estimation accuracies of REMP and the classical estimators. The results indicated that under the non-normal distribution of DEM errors, the classical non-robust estimators are seriously influenced by the non-normality. Some robust estimators such as 10%-trimmed or Winsorized mean and normalized median absolute deviation (MADN) are not very robust to resist the influence of outliers. REMP, slightly affected by the non-normal distribution of DEM errors, is more accurate than the classical estimators. The robust methodology can adapt to the DEMs, especially the ones derived from remote sensing such as LiDAR or digital photogrammetry in non-open terrain.

A high accuracy and speed method (HASM) of surface modelling is developed to find a solution for error problem and to improve computation speed. A digital elevation model (DEM) is established on spatial resolution of 13.5 km x 13.5 km. Regression formulations among temperature, elevation and latitude are simulated in terms of data from 2766 weather observation stations scattered over the world by using the 13.5 km x 13.5 km DEM as auxiliary data. Three climate scenarios of HadCM3 are refined from spatial resolution of 405 km x 270 km to 13.5 km x 13.5 km in terms of the regression formulations. HASM is employed to simulate surfaces of mean annual bio-temperature, mean annual precipitation and potential evapotranspiration ratio during the periods from 1961 to 1990(T(1)), from 2010 to 2039 (T(2)), from 2040 to 2069 (T(3)), and from 2070 to 2099 (T(4)) on spatial resolution of 13.5 km x 13.5 km. Three scenarios of terrestrial ecosystems on global level are finally developed on the basis of the simulated climate surfaces. The scenarios show that all polar/nival, subpolar/alpine and cold ecosystem types would continuously shrink and all tropical types, except tropical rain forest in scenario A1Fi, would expand because of the climate warming. Especially at least 80% of moist tundra and 22% of nival area might disappear in period T(4) comparing with the ones in the period T(1). Tropical thorn woodland might increase by more than 97%. Subpolar/alpine moist tundra would be the most sensitive ecosystem type because its area would have the rapidest decreasing rate and its mean center would shift the longest distance towards west. Subpolar/alpine moist tundra might be able to serve as an indicator of climatic change. In general, climate change would lead to a continuous reduction of ecological diversity. (C) 2010 Elsevier B.V. All rights reserved.

An adaptive method is employed to speed up computation of high accuracy surface modeling (HASM), for which an error indicator and an error estimator are developed. Root mean-square error (RMSE) is used as the error estimator that is formulated as a function of gully density and grid cell size. The error indicator is developed on the basis of error surfaces for different spatial resolutions, which are interpolated in terms of the absolute errors calculated at sampled points while paying attention to the landform characteristics. The error surfaces indicate the magnitude and distribution of errors in each step of adaptive refinement and make spatial changes to the errors in the simulation process visualized. The adaptive method of high accuracy surface modeling (HASM-AM) is applied to simulating elevation surface of the Dong-Zhi tableland with 27.24 million pixels at a spatial resolution of 10 m 10 m. Test results show that HASM-AM has greatly speeded up computation by avoiding unnecessary calculations and saving memory. In addition, HASM-AM improves simulation accuracy.

In addition to classical methods, namely kriging, Inverse Distance Weighting (IDW) and splines, which have been frequently used for interpolating the spatial patterns of soil properties, a relatively more accurate surface modelling technique is being developed in recent years, namely high accuracy surface modelling (HASM). It has been used in the numerical tests, DEM construction and the interpolation of climate and ecosystem changes. In this paper, HASM was applied to interpolate soil pH for assessing its feasibility of soil property interpolation in a red soil region of Jiangxi Province, China. Soil pH was measured on 150 samples of topsoil (0-20 cm) for the interpolation and comparing the performance of HASM, kriging. IDW and splines. The mean errors (MEs) of interpolations indicate little bias of interpolation for soil pH by the four techniques. HASM has less mean absolute error (MAE) and root mean square error (RMSE) than kriging, IDW and splines. HASM is still the most accurate one when we use the mean rank and the standard deviation of the ranks to avoid the outlier effects in assessing the prediction performance of the four methods. Therefore, HASM can be considered as an alternative and accurate method for interpolating soil properties. Further researches of HASM are needed to combine HASM with ancillary variables to improve the interpolation performance and develop a user-friendly algorithm that can be implemented in a GIS package. (C) 2009 Elsevier B.V. All rights reserved.